Problem: Simplify the following expression: $ p = \dfrac{8t - 4}{6t - 1} + \dfrac{-7}{5} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{8t - 4}{6t - 1} \times \dfrac{5}{5} = \dfrac{40t - 20}{30t - 5} $ Multiply the second expression by $\dfrac{6t - 1}{6t - 1}$ $ \dfrac{-7}{5} \times \dfrac{6t - 1}{6t - 1} = \dfrac{-42t + 7}{30t - 5} $ Therefore $ p = \dfrac{40t - 20}{30t - 5} + \dfrac{-42t + 7}{30t - 5} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{40t - 20 - 42t + 7}{30t - 5} $ $p = \dfrac{-2t - 13}{30t - 5}$